A snatch of song, identified

Some years ago I remember very clearly recalling, as if from a dream, a snatch of classical music. I didn't know where I had heard it, or when, but a short, lyrical theme kept playing in my head. This must have been three years ago.
Since then, I have been on a passive search to find it, waiting to hear it on some classical music channel, then hearing the announcer say what it was, and by whom. It plays in my head probably a few times a month.

On Tuesday evening, I heard it on Performance Today. I fairly convulsed as I lurched toward my computer, as if I would be able to read through the sound the name of the elusive piece. But - o me! - it was only an interlude fragment, played between the first and second halves of the show, without identification.

I was not prepared to lose. I went immediately to PT's "contact us" page and explained in the comment box the nature of my quest. I told them that at 30:20 of their March 20th show, they had played part of the piece, and could they please tell me what it was?

I received the following reply, at the end of the school day yesterday:



I immediately searched the symphony, and skipping past the familiar first movement, found my precious gem of a song at the beginning of the second movement.

Here is the video I like the best, of the Seoul Philharmonic. The second movement begins at 7:30, and the theme I searched for is exactly at 7:59, then again at 9:50, where it is led in in the most incredible fashion by the strings, and the flute picks up the theme from them like a wave catching foam, and plays the snatch again. Ah -- ! Unreal.